We construct an entire solution to the elliptic system where is a ‘triple‐well’ potential. This solution is a local minimizer of the associated energy in the sense that minimizes the energy on any compact set among competitors agreeing with outside that set. Furthermore, we show that along subsequences, the ‘blowdowns’ of given by approach a minimal triple junction as . Previous results had assumed various levels of symmetry for the potential and had not established local minimality, but here we make no such symmetry assumptions.

中文翻译：

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无穷远三结结构的艾伦-卡恩解


我们构建了椭圆系统的完整解决方案，其中具有“三井”潜力。该解决方案是相关能量的局部最小化，即最小化与该集合之外的竞争者之间的任何紧凑集合上的能量。此外，我们表明，沿着子序列，通过接近最小三联点给出的“排污”为 。以前的结果假设了势的不同程度的对称性，并且没有建立局部极小性，但在这里我们没有做出这样的对称性假设。